Probability Formula

Probability → Basics → Vocabulary → Probability Formula

The probability of an event can be calculated by the proportion (or probability) formula

$\textrm{Probability}=\frac{\textrm{Favorable events}}{\textrm{Total events}}$

$P=\frac{r}{n}$

For example, in the basic probability vocabulary page, the question was,

Example
A coin is tossed two times. What is the probability that both times the head was occurred?

Answer
Here, the sample space is

$S.S=\{HH,HT,TH,TT\}$

And, the favorable event, or an event for which we want to find probability is $HH$ . This event is 1 among the total 4 events. Hence, $r=1$ and $n=4$ . The probability that both of the events are “heads” is thus

$P(HH)=\frac{1}{4}=0.25$

EXAMPLE 2
A fair dice is rolled once. What is the probability that an even number is occurred?

Answer
If a dice is rolled, any number from 1 to 6 can occur. So, the sample space is

$S.S=\{1,2,3,4,5,6\}$

And even numbers are three: 2,4,6. So favorable events ( $r$ ) are 3, and total events ( $n$ ) are 6. Hence,

$P(\textrm{even number})=\frac{3}{6}=0.5$